In 1988, Kip Thorne et al. demonstrated all traversable wormhole in GR must violate the null energy condition [1]}. It means that the traversable wormholes require exotic matter. The simplest such candidate may be the phantom scalar field. It turns out that phantom fields are one of the most promising candidates of dark energy in cosmology [2]}, [3]}. In particle physics, a phantom field model was proposed to study the neutrino mass generation [4]}. Furthermore, some studies argued that the instability problem of the phantom fields could be curable [5]}.
